Introduction to Classical Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Classical Integrable Systems write by Olivier Babelon. This book was released on 2003-04-17. Introduction to Classical Integrable Systems available in PDF, EPUB and Kindle. This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.
Elements of Classical and Quantum Integrable Systems
Elements of Classical and Quantum Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Elements of Classical and Quantum Integrable Systems write by Gleb Arutyunov. This book was released on 2019-07-23. Elements of Classical and Quantum Integrable Systems available in PDF, EPUB and Kindle. Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.
Introduction to Classical Integrable Systems
Introduction to Classical Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Classical Integrable Systems write by Olivier Babelon. This book was released on 2003-04-17. Introduction to Classical Integrable Systems available in PDF, EPUB and Kindle. A clear and pedagogical introduction to classical integrable systems and their applications. It synthesizes the different approaches to the subject, providing a set of interconnected methods for solving problems in mathematical physics. Each method is introduced and explained, before being applied to particular examples.
An Introduction to Integrable Techniques for One-Dimensional Quantum Systems
An Introduction to Integrable Techniques for One-Dimensional Quantum Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Integrable Techniques for One-Dimensional Quantum Systems write by Fabio Franchini. This book was released on 2017-05-25. An Introduction to Integrable Techniques for One-Dimensional Quantum Systems available in PDF, EPUB and Kindle. This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.
Quantum Integrable Systems
Quantum Integrable Systems - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Quantum Integrable Systems write by Asesh Roy Chowdhury. This book was released on 2004-01-28. Quantum Integrable Systems available in PDF, EPUB and Kindle. The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
